"You know when the guys in Customs start going, 'saw you on the Letterman show', and you're going, 'wow,'" she told CBS News correspondent Anthony Mason.
Her debut album "Eye to the Telescope" sold more than 1 million copies in the U.S. alone and produced a second smash, "Suddenly I See," which proved that the Scottish singer was no one-hit wonder.
Now she is trying to recapture that magic with her sophomore album, "Drastic Fantastic," which is out this week.
Rolling Stone says "Drastic Fantastic" is "crafted with intelligent attention to every detail." But not long ago, Tunstall couldn't get a record deal.
She brings Sunday Morning to her hometown, St. Andrews, Scotland, for a glimpse of the influences that shaped her.